Integrable Complex Structures on Twistor Spaces

Abstract

Abstract We introduce integrable complex structures on twistor spaces fibered over complex manifolds. We then show, in particular, that the twistor spaces associated with generalized Kahler, SKT and strong HKT manifolds all naturally admit complex structures. Moreover, in the strong HKT case, we construct a metric and three compatible complex structures on the twistor space that have equal torsions.